As it was already observed in the work of Rényi ([1]}) and Parry ([2]}), ergodic theory provides a natural unifying framework for dealing with various representations of numbers. As we will see in Section , ergodic approach allows also to prove a rather general theorem which deals with various equivalent forms of normality and has as a quite special corollary the following theorem which summarizes various classical results pertaining to base \(b\)  normality.
